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Are the means for the final exams the same for all statistics class delivery types? Table 13.25 shows the scores on final exams from several randomly selected classes that used the different delivery types.

Consider the null hypothesis that there is no significance difference between the means of final exams from several randomly selected classes. For this, use Ti-83 calculator. For this, click on STAT $→$press $1→$EDIT, then put the above given weights of different groups data into the list localid="1649239399262" $L1,L2andL3$. The screenshot is given as below:

Now Again press STAT $→$arrow over the TESTS $→$arrow down to ANOVA Press var then select $1$, press var then select $2$, and press var then select $3$to fill the values of $L1,L2andL3$. The screen shot is given as below:

Press ENTER. The screenshot of the obtained output of is given as below:

Use the above results to solve the below given subparts.

a. The null hypothesis that three mean commuting mileages are same is given as below:

$H_0:{\mathrm{μ}}_1={\mathrm{μ}}_2={\mathrm{μ}}_3$

b. The alternate hypothesis will be at least any two of the means are different.

c. The degree of freedom in the numerator is $2$, and the degree of freedom in the denominator is $\mathbf{13}\mathbf{.}$

d. The $F$distribution is used for the test of three different means.

e. The value of the test statistic is .$0.6388$ .

f. The $P$-value for the test is $\mathbf{0}\mathbf{.}\mathbf{54}$.

g. The graph of the distribution is given as below:

h.

a. Level of significance $\mathrm{Î\pm }$is $0.05$.

b. Decision: Null hypothesis will be accepted.

c. Reason for decision: $P$-value is $0.54$, which is greater than the $0.05$level of significance.

d. The means of final exams scores from several randomly selected classes are the same.

We accept the null hypothesis.